To get married in Hawaii there is no waiting period and no blood tests, you just fill out the marriage license application online, and prepay it, then make a note of the confirmation number they will give you.
If either of you have ever been married before you just need to know the date and county where the divorce was final, if it is within 60 days of your new marriage, bring documentation.
The State Department of Health is at 1250 Punchbowl in downtown Honolulu on the corner of Beretania and Punchbowl across from the state capitol building. It is first come, first served, but if you go in early enough you will be in and out in fifteen minutes! Both of you need to be present to pick up the marriage license and you will need to show ID.
The application will ask for the first, middle and last name of your biological father and the first, middle and MAIDEN name of your biological mother. One of the reasons for this is to provide information for future generations who may be tracing their lineage. As I explained to one of my brides, some kid in 2525 who is researching her lineage may be working on something important and need to have the biological information of her heritage. So when you are filling this out, give a silent nod to that curious child of the future, who will someday look for, and find, you.
A word about receiving your official marriage license from the State Department of Health sooner than one to two months after the wedding: As of January 2012, registered officiants go online after the wedding to validate the marriage license and a temporary copy of the license is available to print out within three working days, however, it is only good for three months and by then you should have received the official one in the mail. To get an official copy right away, there is a certified copy request you may fill out online and prepay, then pick up at Vital Records at 1250 Punchbowl once the license has gone to vital records. They will give it to you on the spot, you don't even have to wait in line! Here is the link: